1. Field of the Invention
The present invention relates to computerized methods and apparatus for creating particle packs and, more specifically, to computerized methods and apparatus for creating particle packs with enhanced speed and processing efficiency.
2. Description of the Related Art
The present invention relates to the creation of particle packs that can be used to model or simulate particle containing or particle filled systems. There are many varieties of particle containing systems. Specific yet merely illustrative examples are found in the fields of asphalts, concretes, ceramics, soils, chemical physics of amorphous materials, slurry mechanics, and solid propellants or gas generators. An important class of such systems comprises polymeric materials with particles embedded or embodied in the polymer body or binder.
It is highly desirable in many circumstances to have a capability to model or simulate the properties, performance, etc. of such particle containing systems. In designing such particle filled systems, for example, substantial trial and error can be avoided if one is able to use a model or simulation to assess the implications of making changes in the components, their configuration, the conditions, etc.
This is particularly true in microstructural analyses, e.g., wherein the analysis focuses on the material at a highly magnified level, such as at the molecular or grain stages. A specific example of microstructural analysis would involve the modeling or simulation of a particle pack for a propellant, which typically would include fuel and oxidizer particles in a polymeric binder. When modeling or simulating a particle containing system, it has become customary to construct an analytical replica or representation of the particle filled material, which is generally referred to as a particle pack. The term “particle pack” has come to be used in the field to refer generally to a collection of particles in a defined volume.
The general object in creating particle packs is to model or simulate the manner in which a plurality of particles, usually a large number of such particles, will fill or otherwise occupy a particular space. The nature of the particles may vary, in some cases considerably, depending on the particular application. These variations may include particle size variations, as well as other characteristics.
The complexity of models used to simulate real world particle containing systems increases dramatically if more than a limited number of variables are considered. The numbers of interactions, combinations and permutations brought to bear by anything other than relatively simple systems causes the processing requirements to become unwieldy even for the most advanced computer systems. This complexity and processing requirement limitation is even more pronounced for systems that employ large numbers of particles.
These limitations have caused workers in the field to invoke various simplifying assumptions to render the problem more workable. One such assumption involves the shape of the particle. The complexity and related processing demands can be substantially reduced, for example, if one assumes that the particles are spherical.
The general approach to simulating particle containing systems in the past has involved a more rigorous one in which a particle pack is constructed by placing the individual particles into a three dimensional volume, i.e., into a “full field.” This approach in theory offers promise for accurate simulation of the real particle containing systems. The large number of particles required to construct a statistically meaningful or useful particle pack, however, usually renders this approach impractical. The processing power required to construct such a particle pack is prohibitive for all but extremely small numbers of particles, and only relatively small variations in particle size.
The simplifying assumptions necessary to reduce processing demands down to a manageable level can prevent the resulting particle pack from accurately portraying the actual packs that are intended to be simulated.
An approach that has been used to make the processing demands more manageable and yet the accuracy and reliability of the simulation to be good involves a reduced dimension approach. An example of this approach is described in I. Lee Davis and Roger G. Carter, “Random Particle Packing by Reduced Dimension Algorithms,” J. Appl. Phys., 67(2), 15 Jan. 1990 pp. 1022-1029 (hereinafter “Davis and Carter”). The reduced dimension approach as described there involves simplifying the pack construction problem by employing the principle that an arbitrary straight line drawn through a uniformly random three-dimensional particle pack (regardless of whether the particles are spheres) will, on the average, lie inside particles the same fraction of its length as the packing fraction. As the length of the line goes to infinity, the fraction of its length residing inside the particles of a random pack goes to the packing fraction exactly. The line is referred to in Davis and Carter as a “central string.” This approach has proven quite useful in enabling more complicated particle packs to be constructed. It can accommodate a substantially wider range of particle sizes.
Notwithstanding the usefulness of the reduced dimension approach to constructing particle packs, its direct application has been limited to a certain extent in that its accuracy can be compromised by considering only particles intersected by the central string. In real three-dimensional packs, and assuming the particles are spherical, each sphere initially intersecting the central sphere, as it slides down the central string during placement, comes to rest more often on a “nearest-neighbor” sphere than on a lower central string particle. The sphere then would roll away from the central string, thereby spreading the spheres over a greater distance along the central string.
A technique for addressing this limitation, also presented in the Davis and Carter paper noted above, involves relaxing the requirement that spheres must intersect the central. Under this modified approach, particles are permitted to come to rest within a defined range of the central string, after assuming that their path is modified to encounter and avoid previously placed spheres. This is referred to generally as “perturbation,” or perturbed central string packing.
This modified reduced dimension approach also has been limited, however, in that, when perturbation approaches are used, processing demands once again increase, in some cases substantially. This can give rise to a fuller and more complicated particle field that once again begins to approach the complexity and processing intensity of a full field.
Accordingly, it would be desirable to provide apparatus and methods for creating a particle pack that simulate the actual particle distribution within a space with a reasonable degree of accuracy.
It would also be desirable to provide apparatus and methods for creating a particle pack that involve reduced processing demands and increased processing efficiency relatively to full field simulation.
Advantages of the invention will be apparent from the description, or may be learned by practice of the invention in accordance therewith. The advantages of the invention may be realized and obtained by means of the instrumentalities and combinations pointed out in the appended claims.